For those who don’t systematically open 1NT with a five-card major, the sequence 1♦– 2♣ is a little peculiar, in as much as the opener cannot hold 15-17 HCP and a regular hand. Therefore, no-trump rebids are not the same as after a major suit opening. Contrary to a wide-spread (but obviously false) thought, responder can still have a fourcard major when he bids 2♣: thus, a 4-4 fit in a major is still possible.
With 11HCP West has enough to bid a new suit at the two-level, but not enough to force to game.
He has an adequate bid at hand to show his six beautiful Clubs and a limited hand: he repeats his suit at the three-level.
This bid is non-forcing and East, who has a minimum, is quick to pass.
Opposite West’s reverse, East notes the fit and must not forget to count his distribution points: he now has a hand worth 17 points. The only bid to set Spades as trumps while showing slam interest is a raise to the three-level. Now all that is left to do is proceed with the usual verifications: control bids and RKCB.